When using manipulatives in math education, it is important to hold all students accountable throughout the activity. I would manage this challenge by first posing a question in conjunction with the manipulative for the students to consider. Then I would circulate the classroom asking more questions as necessary to keep the students thinking mathematically. I might also have students record their thinking the way we did during our manipulative activity in ETE 339.
Another point to consider in math education is the concept of "hands-on, minds-on" learning. While hands-on activities successfully engages students and prevents them from disrupting the classroom flow, the hands-on activities should also engage the students cognitively. Not only should the students explore with manipulative materials, they should think about the mathematical processes involved with the manipulative.
Using manipulatives in math education can easily involve all five process standards. Students use manipulatives to create and explore a variety of representations of math concepts. Manipulatives enable students to connect math concepts between the five content areas, guiding them to understand that math is not a host of disjointed ideas, but a network of interconnecting ideas. Working with manipulative materials lends itself to students working in pairs or small groups, enabling communication about math concepts among the individuals in the group. Manipulatives serve as a tool for students to use when explaining math processes, and teachers can provide manipulatives for students to use when solving problems, as manipulatives often include generous opportunities for activating prior knowledge to form new knowledge.
Wednesday, April 28, 2010
Monday, April 26, 2010
Error Analysis
I thought that the error analysis activities were some of the most beneficial aspects of the math methods course. It had not occurred to me before to look for patterns in the students' errors. I also really enjoyed learning different ways to teach addition, subtraction, multiplication, and division. I learned that often, the reasons students make errors is because they do not understand the processes of their problems. They simply try to memorize the process.
In my future classroom, I anticipate teaching students through the use of manipulatives and multiple representations so that my students more completely understand the operations they perform. I also would like to apply the way Dr. Grant taught us to teach the algorithms because I think that way makes more sense than the way I was taught. Finally, I hope to remember to look for patterns in my students errors, as those patterns provide insight to the students' thinking and can provide direction for me as a teacher.
In my future classroom, I anticipate teaching students through the use of manipulatives and multiple representations so that my students more completely understand the operations they perform. I also would like to apply the way Dr. Grant taught us to teach the algorithms because I think that way makes more sense than the way I was taught. Finally, I hope to remember to look for patterns in my students errors, as those patterns provide insight to the students' thinking and can provide direction for me as a teacher.
Friday, April 23, 2010
Technology
The most useful forms of technology that I used in Math Methods were the basic communication tools - Google Docs and email. Working with large groups of people, it would have been a nightmare to prepare our projects without Google Docs. There was a number of times when several of us were editing the Google Docs at once - something we could not do with the Wiki. We also used email and chat extensively to communicate about meeting times and questions regarding our projects. These two tools - Google Docs and email - were life-savers for this class.
Other technology sources that we used included the wiki page, smart board, Geometer's Sketchpad, calculators, Sakai forums, and NCTM resources. The wiki page was frustrating because only one person could edit at a time. Therefore, if one person had three or four hours of information to add to the wiki, the other group members were handicapped for that period of time unless they stole the lock from the other person. If they chose to steal the lock, the other person's information would be lost. Google Docs was far superior to the wiki. The smart board is a tool that I have already used in Novice Teaching, and I presume that I will be using it in my future occupation. I appreciated the opportunities in Math Methods to play around with smart board. Geometer's Sketchpad is an excellent tool for helping students grasp geometry concepts without having to create their own representations by hand. Learning about this tool was very beneficial, and I can see myself using it in my own classroom some day. The calculators that could figure fractions are a long-time awaited invention. Now students will be able to discover math instead of simply doing math, by experimenting with LCM, GCF, adding, subtracting, multiplying, and dividing fractions, and other information regarding fractions. The Sakai forums were a useful tool for claiming our articles, although it would have been just as easy to send and email to relate that information. Finally, the NCTM website was great, with its vast resources including applets and illuminations. I am excited to know of such a rich resource where I can find activities to supplement or teach math concepts.
Overall, the use of technology in Math Methods had given me tools to fulfill the following quote: "The art of teaching is the art of assisting discovery." I look forward to using technology in the future as a means to "assist discovery" in my students.
Other technology sources that we used included the wiki page, smart board, Geometer's Sketchpad, calculators, Sakai forums, and NCTM resources. The wiki page was frustrating because only one person could edit at a time. Therefore, if one person had three or four hours of information to add to the wiki, the other group members were handicapped for that period of time unless they stole the lock from the other person. If they chose to steal the lock, the other person's information would be lost. Google Docs was far superior to the wiki. The smart board is a tool that I have already used in Novice Teaching, and I presume that I will be using it in my future occupation. I appreciated the opportunities in Math Methods to play around with smart board. Geometer's Sketchpad is an excellent tool for helping students grasp geometry concepts without having to create their own representations by hand. Learning about this tool was very beneficial, and I can see myself using it in my own classroom some day. The calculators that could figure fractions are a long-time awaited invention. Now students will be able to discover math instead of simply doing math, by experimenting with LCM, GCF, adding, subtracting, multiplying, and dividing fractions, and other information regarding fractions. The Sakai forums were a useful tool for claiming our articles, although it would have been just as easy to send and email to relate that information. Finally, the NCTM website was great, with its vast resources including applets and illuminations. I am excited to know of such a rich resource where I can find activities to supplement or teach math concepts.
Overall, the use of technology in Math Methods had given me tools to fulfill the following quote: "The art of teaching is the art of assisting discovery." I look forward to using technology in the future as a means to "assist discovery" in my students.
Monday, April 12, 2010
Supporting Language Learners
Supporting Language Learners from Teaching Children Mathematics
This article suggests two methods of assisting language learners in the mathematics classroom. One method involves helping the students through their English language acquisition. Some strategies include using advanced organizers, bi-lingual organizers, explaining mathematical terms as homonyms (some,sum), visual cues, and adjusting teacher talk (repeating, slowing down, simplifying, consistency, and avoiding idioms). The article discussed two tasks which assist language learners in developing their terminology. One involved a story with manipulatives relating to the story (fishing) and checked the students' understanding of "more than" and "less than." The other activity shows how teachers can change the wording of directions to a problem to be more consistent with language learners vocabulary. A second method of helping language learners in the classroom is to promote a low-anxiety classroom environment. Teachers should reassure the language learner that mistakes are common. They should teach their students how to applaud and praise each other rather than ridicule mistakes. Routines also help language learners feel comfortable in the classroom - knowing what will come next in the day. Finally, teachers should use signals and assign classroom buddies to ease tension that language learners may feel .
I have already had the opportunity to apply some of these strategies - not with language learners, but with a student with Asperger's syndrome who struggled processing words and dictating his thoughts. I noticed that assisting him with understanding words was always necessary, regardless of the subject. He was an intelligent child, but simply needed extra help with vocabulary. I also noticed that he performed much higher when he was at ease in the classroom. If he felt like his peers were watching him or making fun of him, he lost all ability to function. I am sure that language learners will pose different experiences than I had with this student, but I do believe that applying the strategies for making the classroom a comfortable place and helping them with their vocabulary will assist them greatly in mathematics.
This article suggests two methods of assisting language learners in the mathematics classroom. One method involves helping the students through their English language acquisition. Some strategies include using advanced organizers, bi-lingual organizers, explaining mathematical terms as homonyms (some,sum), visual cues, and adjusting teacher talk (repeating, slowing down, simplifying, consistency, and avoiding idioms). The article discussed two tasks which assist language learners in developing their terminology. One involved a story with manipulatives relating to the story (fishing) and checked the students' understanding of "more than" and "less than." The other activity shows how teachers can change the wording of directions to a problem to be more consistent with language learners vocabulary. A second method of helping language learners in the classroom is to promote a low-anxiety classroom environment. Teachers should reassure the language learner that mistakes are common. They should teach their students how to applaud and praise each other rather than ridicule mistakes. Routines also help language learners feel comfortable in the classroom - knowing what will come next in the day. Finally, teachers should use signals and assign classroom buddies to ease tension that language learners may feel .
I have already had the opportunity to apply some of these strategies - not with language learners, but with a student with Asperger's syndrome who struggled processing words and dictating his thoughts. I noticed that assisting him with understanding words was always necessary, regardless of the subject. He was an intelligent child, but simply needed extra help with vocabulary. I also noticed that he performed much higher when he was at ease in the classroom. If he felt like his peers were watching him or making fun of him, he lost all ability to function. I am sure that language learners will pose different experiences than I had with this student, but I do believe that applying the strategies for making the classroom a comfortable place and helping them with their vocabulary will assist them greatly in mathematics.
Making Technology Work
Making Technology Work from Mathematics Teaching in the Middle School
This article encourages teachers to ensure that their use of technology follows this criteria: it allows students to do something they could not have done before, or it allows students to do something they could do before in a better way. It warns against using technology when students could perform a task more quickly without the technology; yet it promotes using technology to help students use higher-level thinking and to visualize math better. The article provides an example of a beneficial use of technology - The Weather Project. In this project, the students must create a pamphlet about the weather in five different regions of Croatia. The project not only connects to other subject areas, it allows students to work with real data and to use technology to interpret and represent the data. The students took ownership in the project because it was a real to life experience.
I appreciated that this article addressed the need to use technology wisely. Technology can be powerful, but it can also be debilitating if it does not meet the criteria for beneficial uses of technology. If I take anything from the article, it will be to ask myself as a future teacher whether my desire to use technology truly allows students to do something they would not be able to do otherwise. Does the technology promote higher-level thinking? Will it enable students to engage in real-world applications of mathematics? Will it engage students in exploration and discovery? Technology cannot replace the brain - and teachers must be careful that they use it in a way that enhances learning.
This article encourages teachers to ensure that their use of technology follows this criteria: it allows students to do something they could not have done before, or it allows students to do something they could do before in a better way. It warns against using technology when students could perform a task more quickly without the technology; yet it promotes using technology to help students use higher-level thinking and to visualize math better. The article provides an example of a beneficial use of technology - The Weather Project. In this project, the students must create a pamphlet about the weather in five different regions of Croatia. The project not only connects to other subject areas, it allows students to work with real data and to use technology to interpret and represent the data. The students took ownership in the project because it was a real to life experience.
I appreciated that this article addressed the need to use technology wisely. Technology can be powerful, but it can also be debilitating if it does not meet the criteria for beneficial uses of technology. If I take anything from the article, it will be to ask myself as a future teacher whether my desire to use technology truly allows students to do something they would not be able to do otherwise. Does the technology promote higher-level thinking? Will it enable students to engage in real-world applications of mathematics? Will it engage students in exploration and discovery? Technology cannot replace the brain - and teachers must be careful that they use it in a way that enhances learning.
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